We describe limit fluctuations of the height function for the open TASEP on the coexistence line under the stationary measure. It is known that the height function satisfies a law of large numbers as the number of sites $n$ goes to infinity which at the coexistence line is exotic in the sense that the first-order limit is random. Here, we study the functional central limit theorem: we show that with a random centering and normalized by $\sqrt n$, the second-order limit of the height functions is a (random) mixture of two independent Brownian motions.